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Benchmarking Chart

PurposeThe Benchmarking Chart provides both a graphical and a quantitative way to compare productsand processes against each other on the common baseline of the Sigma scale of measure.

Anatomy

Six Sigma - Tools & Concepts BenchCha_001

The Benchmarking Chart

# of Parts

(Steps) 3 4 5 6

1 93.32% 99. 379% 99.9767% 9 9.99966%7 61.63 95.733 99.839 99.9976

10 50.08 93.96 99.768 99.9966

20 25.08 88.29 99.536 99.993240 6.29 77.94 99.074 99.986460 1.58 68.81 98.614 99.979680 0.40 60.75 98.156 99.9728

100 0.10 53.64 97.70 99.966150 -- 39.38 96.61 99.949200 -- 28.77 95.45 99.932300 -- 15.43 93.26 99.898400 -- 8.28 91.11 99.864500 -- 4.44 89.02 99.830600 -- 2.38 86.97 99.796700 -- 1.28 84.97 99.762800 -- 0.69 83.02 99.729900 -- 0.37 81.11 99.695

1000 -- 0.20 79.24 99.6611200 -- 0.06 75.88 99.5933000 -- -- 50.15 98.985

17000 -- -- 0.02 94.38438000 -- -- -- 87.88070000 -- -- -- 78.820

150000 -- -- -- 60.000

(Distribution Shifted 1.5)

PagerPager

Sales ErrorsSales Errors

Data ClocksData Clocks

PhonePhone

TelevisionTelevision

Disc MemoryDisc Memory

PortablePhone

PortablePhone

Rolled

Yield

Complexity(part count or process steps)

Process

Capability

B

A

C

D

Reference:

TerminologyA. Process Complexity - The number of steps, or manufactured parts, in the product or

process.B. Process Capability - The Sigma, or Z scale of measure.C. Rolled Throughput Yield - The running mathematical product of all the individual process

step (throughput) yields in a process.D. Benchmarking Point - The point plotted on the Benchmarking table, intersecting the

achieved level of process/product complexity, Sigma, and Rolled Throughput Yield.

Major Considerations

Application Cookbook1. The Benchmarking Chart is easily constructed once the necessary raw input data has been

collected. The first step in the construction of the chart is to prepare the underlying table.The Complexity/Sigma/Rolled Yield table is laid out as per the following formulae:STEPS SIGMA VALUES

3 4 5 6

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1 Rolled Yield = (NORMSDIST(Sigma-1.5))^(# of Steps)7 . . . .10 . . . .20 . . . .etc. . . . .

2. Once the underlying table has been generated, then the last step is to plot the individual

benchmark values over the tabulated Rolled Yield values, corresponding to the attainedSigma/Complexity/Rolled Yield value of the benchmarked points.

3. Interpretation - The benchmark diagram on the preceding page, for example, shows pointsplotted for a variety of electronics products. We can see that most of the items are around 4Sigma, with "Disc Memory" approximately 5 Sigma. Note also the relative complexity of theproducts, with "Data Clocks" being comparatively simple with only about 10 steps, while"Portable Phones" are very complex items, requiring approximately 17,000 production steps.It is also apparent that the two items labeled "Phone" and Disc Memory", are approximatelyequal in complexity, yet the "Phone" is only 4 Sigma, while the "Disc Memory" is produced ata much better 5 Sigma level.